Problem: Which of these numbers is prime? ${11,\ 36,\ 45,\ 81,\ 85}$
Solution: A prime number has exactly two factors: 1 and itself. The factors of 11 are 1 and 11. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 45 are 1, 3, 5, 9, 15, and 45. The factors of 81 are 1, 3, 9, 27, and 81. The factors of 85 are 1, 5, 17, and 85. Thus, 11 is a prime number.